Feb 3, 2017 · Where [itex]m_o[/itex] is the initial mass of the fueled up rocket, and [itex]-k[/itex] is the rate at which mass leaves the rocket. Also, [itex]u[/itex] is the velocity of the exhaust (which is taken as a constant), and [itex]v[/itex] is the velocity of the rocket itself. For linear drag + gravity, the resultant equation of motion would be:

Sep 20, 2005 · Problem: A rocket ejects mass at a constant speed u in its rest frame. Find the ratio of the initial and final rest masses of the rocket in terms of u and the final speed v. (Note: In both methods I'll be using c=1 units) Method 1: Let O be the rest frame of the rocket at some time. The rocket ejects a small mass dM at velocity u.

Jan 7, 2017 · Homework Statement In Newtonian mechanics, the rocket equation is derived by solving the simple differential equation -dm U = m dV, where U is the velocity of the expelled material relative to the rocket; a matter of conservation of momentum. In order to get the correct relativistic equation...

May 30, 2021 · @greg_rack please note that your previous question on the relativistic rocket equation is really the same question as your more recent one on the velocity of an accelerating object; the rocket is the accelerating object. Accordingly, as noted just above, your two threads on that topic have been combined under the "relativistic rocket equation ...

May 27, 2021 · For rockets, thruster, I found the Tsiolkovsky rocket equation: $$\Delta v=v_e ln(\frac{m_0}{m_f})$$ Of course, rockets can travel up to relativistic speeds, thus a relativistic implementation of the RE must be taken into account for a higher degree of accuracy in …

Dec 10, 2009 · Ciolkovski's formula, also known as the Tsiolkovsky rocket equation, is a mathematical formula that describes the motion of a rocket in terms of its velocity, mass, and exhaust velocity. It was derived by Russian scientist Konstantin Ciolkovski in the late 19th century and is a fundamental equation in rocket science.

Jul 10, 2017 · The first equation does not refer to Mass Ejection Rate. If the Mass Ejection Rate (MER) is too small the thrust will not be sufficient for the rocket to take off. Increasing the MER one might get: Rocket takes off once Thrust > Weight Rocket takes off immediately at …

Feb 25, 2011 · First, get the rocket equation as a function of time, and then integrate that. V = delta-V V e = exhaust velocity mdot = mass flow rate M 0 = initial total mass including propellant M = mass without propellant M 0 / M = mass ratio D = distance travelled (1) M = M 0 - mdot * t Substituting for M in the rocket equation V = V e * log(M 0 / M)

Nov 27, 2016 · The rocket equation, also known as the Tsiolkovsky rocket equation, is a mathematical equation that describes the motion of a rocket in terms of its mass and the exhaust velocity of its propellant. It is important in space travel because it helps calculate the amount of propellant needed to reach a certain velocity and altitude, and also ...

Feb 11, 2024 · a) Before a rocket begins to burn fuel, the rocket has a mass of ##m_{r,i}=2.81\times 10^7\mathrm{kg}##, of which the mass of fuel is ##m_{f,i}=2.46\times 10^7\mathrm{kg}##. The fuel is burned at a constant rate with total burn time ##\mathrm{510s}## and ejected at a speed of ##u=3000\mathrm{m/s}## relative to the rocket.